Robust Model and Solution Algorithm for the Railroad Blocking Problem under Uncertainty

Abstract

The railroad blocking problem emerges as an important issue at the tactical level of planning in freight rail transportation. This problem consists of determining the optimal paths for freight cars in a rail network. Often, demand and supply resource indicators are assumed to be certain, so the solution obtained from a certain model might not be optimal or even feasible in practice because of the stochastic nature of these parameters. To address this issue, this paper develops a robust model for this problem with uncertain demand and uncertain travel time as supply resource indicators. Since the model combines integer variables and nonlinear functions, a branch-and-cut algorithm is used to solve the linearized version of the robust model. The performance of the proposed algorithm in several instances is discussed. A comparison with a well-known solver shows the high efficiency and effectiveness of the proposed algorithm. Finally, this algorithm is applied to a blocking problem of the railways of Iran. The results show that, by ignoring approximately 10% of the optimal value of the deterministic model, we have an optimal solution that remains unchanged with a probability of more than 0.98.